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Laws Of Motion

Question
CBSEENPH11020597

Two sphere A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along the x -axis. After the collision, B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction

  • same as that of B

  • opposite to that of B

  • straight theta space equals space tan to the power of negative 1 end exponent space open parentheses 1 half close parentheses space to space the space straight x space minus axis
  • straight theta space equals space tan to the power of negative 1 end exponent space open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses space to space the space straight x space minus axis

Solution

C.

straight theta space equals space tan to the power of negative 1 end exponent space open parentheses 1 half close parentheses space to space the space straight x space minus axis

Here, Pi = m2vi +m2 x 0

straight P subscript straight f space equals space straight m subscript 2 straight v over 2 straight j space plus space straight m subscript 1 space straight x space straight v subscript 2
Law space of space conservation space of space momentum
straight P subscript straight i space equals space straight P subscript straight f
straight m subscript 2 straight v subscript straight i space equals straight m subscript 2 space straight v over 2 straight j space plus straight m subscript 1 straight x space straight v subscript 1
straight v subscript 1 space equals space fraction numerator straight m subscript 2 over denominator straight m subscript 1 space end fraction vi space plus straight m subscript 2 over straight m subscript 1 straight v over 2 straight j
From space this space equation space we space can space find
tan space straight theta space equals space 1 half
straight theta space equals space tan to the power of negative 1 end exponent space open parentheses 1 half close parentheses space to space the space straight x minus space axis